Calm female with arrogant male

I'm looking for a manga that has a calm/strong female with an arrogant/cynical male duo? Preferably with supernatural themes, but that doesn't really matter. And it doesn't have to be romantic duo either. I'm open to everything, just as long as the protangonist isn't a sympathy-hungry sap.

Some examples that I can think of would be:Karakuri Odette - Odette and AsaoSiestaInuyasha - Kagome and Inuyasha

Heart no Kuni no Alice perhaps- it's a cold/calm Alice and the male leads tend to be very arrogant. Though it is rather reverse harem, the manga does sort of wrap up who she'll end up with. Be warned it gets a bit confusing, though, so you may want to read an explanation/summary.

Kamisama Hajimemashita if you've not read it yet. 'Calm' is debatable, though she's got a good head on her shoulders. But personally I think he's arrogant all the way.

Koi Dano Ai Dano and it's prequel. She's calm I suppose... but maybe as arrogant as him? They're a good couple, haha. No supernatural.

her majesty's dog - I think. The female is certainly calm (although maybe 'cold' is a better term). I think the male lead is arrogant but could be wrong, its been ages since I touched it. its supernatural.